Linear independence measures for Chowla--Selberg periods

Abstract

We use simultaneous Padé approximations to ${}_3{F}_2$ hypergeometric functions to estimate from below linear forms in $1$, $\pi \sqrt{d}$, ${\Omega }_D/\pi$ and $\pi /{\Omega }_D$ with integral coefficients, for certain choices of positive integer $d$ and negative integer $D$, where ${\Omega }_D$ is (the square of) a Chowla--Selberg period attached to the imaginary quadratic field $Q(\sqrt{D})$.

arXiv comment4 pages